# Siberian Advances in Mathematics

## Description

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- Other titlesSiberian advances in mathematics (Online), Siberian advances in mathematics
- ISSN1934-8126
- OCLC76708366
- Material typeDocument, Periodical, Internet resource
- Document typeInternet Resource, Computer File, Journal / Magazine / Newspaper

## Publications in this journal

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**ABSTRACT:**It's established a series of convegence theorems of spatial mappingsSiberian Advances in Mathematics 12/2013; 23(4). -
##### Article: An integral representation and boundary behavior of functions defined in a domain with a peak

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**ABSTRACT:**We establish an invertible characteristic of boundary behavior of functions in Sobolev spaces defined in a space domain with a vertex of a peak on the boundary.Siberian Advances in Mathematics 01/2011; 21(2):130-159. - [Show abstract] [Hide abstract]

**ABSTRACT:**We obtain two new equivalent quasinorms for unweighted isotropic Besov and Lizorkin-Triebel spaces in the epigraph of a Lipschitz function. The question on the straightening is studied, i. e., the question on the existence of a diffeomorphism taking the epigraph into a halfspace which preserves the Lizorkin-Triebel spaces of the same indices. A criterion for the straightening is established in terms of dyadic weighted inequality where oscillations of a given function on stretched dyadic cubes are involved.Siberian Advances in Mathematics 01/2011; 21(2):100-129. -
##### Article: On a problem by V. A. Toponogov

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**ABSTRACT:**We give the positive solution of a problem formulated by V. A. Toponogov and discuss some of its natural generalizations.Siberian Advances in Mathematics 01/2011; 21(3):170-175. -
##### Article: On a semilattice of numberings

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**ABSTRACT:**We study some properties of a $$ \mathfrak{c} $$-universal semilattice $$ \mathfrak{A} $$ with the cardinality of the continuum, i.e., of an upper semilattice of m-degrees. In particular, it is shown that the quotient semilattice of such a semilattice modulo any countable ideal will be also $$ \mathfrak{c} $$-universal. In addition, there exists an isomorphism $$ \mathfrak{A} $$ such that $$ {\mathfrak{A} \mathord{\left/ {\vphantom {\mathfrak{A} {\iota \left( \mathfrak{A} \right)}}} \right. \kern-\nulldelimiterspace} {\iota \left( \mathfrak{A} \right)}} $$ will be also $$ \mathfrak{c} $$-universal. Furthermore, a property of the group of its automorphisms is obtained. To study properties of this semilattice, the technique and methods of admissible sets are used. More exactly, it is shown that the semilattice of mΣ-degrees $$ L_{m\Sigma }^{\mathbb{H}\mathbb{F}\left( S \right)} $$ on the hereditarily finite superstructure $$ \mathbb{H}\mathbb{F} $$(S) over a countable set S will be a $$ \mathfrak{c} $$-universal semilattice with the cardinality of the continuum.Siberian Advances in Mathematics 01/2010; 20(2):128-154. - [Show abstract] [Hide abstract]

**ABSTRACT:**We describe simple sufficient conditions on tomography-type measurements of a planar set which imply convexity of this set. The cases of partial convexity and higher-dimensional sets are considered as well.Siberian Advances in Mathematics 01/2009; 19(2):85-90. -
##### Article: An analytic representation of the L 0 -valued homomorphisms in the Orlicz-Kantorovich modules

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**ABSTRACT:**We consider the Orlicz-Kantorovich modules L M (∇,m) associated with a complete Boolean algebra ∇, an N-function M, and a measure m defined on ∇ and taking values in the algebra L 0 of all measurable real functions. We obtain an analytic representation of the continuous L 0-valued homomorphisms defined on such modules.Siberian Advances in Mathematics 01/2009; 19(2):128-149. - [Show abstract] [Hide abstract]

**ABSTRACT:**Let Ω1, Ω2 ⊂ ℝν be compact sets. In the Hilbert space L 2(Ω1 × Ω2), we study the spectral properties of selfadjoint partially integral operators T 1, T 2, and T 1 + T 2, with $$ \begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered} $$ whose kernels depend on three variables. We prove a theorem describing properties of the essential and discrete spectra of the partially integral operator T 1 + T 2.Siberian Advances in Mathematics 01/2009; 19(4):233-244. - [Show abstract] [Hide abstract]

**ABSTRACT:**Let Ω = [a, b] ν and let T be a partially integral operator defined in L 2(Ω2) as follows: $$ (Tf)(x,y) = \int_\Omega {q(x,s,y)f(s,y)} d\mu (s). $$ In the article, we study the solvability of the partially integral Fredholm equations f − ℵTf = g, where g ∈ L 2(Ω2) is a given function and ℵ ∈ ℂ. The notion of determinant (which is a measurable function on Ω) is introduced for the operator E − ℵT, with E is the identity operator in L 2(Ω2). Some theorems on the spectrum of a bounded operator T are proven.Siberian Advances in Mathematics 01/2009; 19(3):151-161. - [Show abstract] [Hide abstract]

**ABSTRACT:**The article contains the proofs of two theorems. Under quite special assumptions, we prove that the p-cyclic extensions of Henselian valued fields are defect-free. However, the well-known results by Epp and Kuhlmann are easy consequences of these theorems.Siberian Advances in Mathematics 01/2008; 18(1):30-43. - [Show abstract] [Hide abstract]

**ABSTRACT:**Let a piece of the boundary of a Lipschitz domain be parameterized conventionally and let the traces of functions in the Sobolev space W p 2 be written out through this parameter. In this space, we propose a discrete (diadic) norm generalizing A. Kamont’s norm in the plane case. We study the conditions when the space of traces coincides with the corresponding space for the plane boundary.Siberian Advances in Mathematics 01/2008; 18(4):258-274. -
##### Article: Superlarge deviations for sums of random variables with arithmetical super-exponential distributions

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**ABSTRACT:**Local limit theorems are obtained for superlarge deviations of sums S(n) = ξ(1) + ... + ξ(n) of independent identically distributed random variables having an arithmetical distribution with the right-hand tail decreasing faster that that of a Gaussian law. The distribution of ξ has the form ℙ(ξ = k) = $$ e^{ - k^\beta L(k)} $$, where β > 2, k ∈ ℤ (ℤ is the set of all integers), and L(t) is a slowly varying function as t → ∞ which satisfies some regularity conditions. These theorems describing an asymptotic behavior of the probabilities ℙ(S(n) = k) as k/n → ∞, complement the results on superlarge deviations in [4, 5].Siberian Advances in Mathematics 01/2008; 18(3):185-208. - [Show abstract] [Hide abstract]

**ABSTRACT:**We study some categorical properties of the functor O β of weakly additive functionals acting in the category Tych of the Tychonoff spaces and their continuous mappings. We show that O β preserves the weight of infinite-dimensional Tychonoff spaces, the singleton, and the empty set, and that O β is monomorphic and continuous in the sense of T. Banakh, takes every perfect mapping to an epimorphism, and preserves intersections of functionally closed sets in a Tychonoff space.Siberian Advances in Mathematics 01/2007; 17(4):291-296. - [Show abstract] [Hide abstract]

**ABSTRACT:**Locally homogeneous Riemannian spaces were studied in [1–4]. Locally conformally homogeneous Riemannian spaces were considered in [10]. Moreover, the theorem claiming that every such space is either conformally flat or conformally equivalent to a locally homogeneous Riemannian space was proved. In this article, we study locally conformally homogeneous pseudo-Riemannian spaces and prove a theorem on their structure. Using three-dimensional Lie groups and the six-dimensional Heisenberg group [11], we construct some examples showing the difference between the Riemannian and pseudo-Riemannian cases for such spaces.Siberian Advances in Mathematics 01/2007; 17(3):186-212. - [Show abstract] [Hide abstract]

**ABSTRACT:**English translation of Mat. Tr. 5, No. 2, 138–154 (2002; Zbl 1012.54037).Siberian Advances in Mathematics 01/2004; 14(3). -
##### Article: Generic automorphisms

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**ABSTRACT:**We study generic sequences of automorphisms. For some classes of models (for example, saturated models), we show that every sequence of automorphisms whose length does not exceed the cardinality of the model is the element-wise product of two sequences. We also prove that the fixed field of a finite generic sequence of automorphisms of a separably closed field is regularly closed. This is an English translation of the author’s article [Mat. Tr. 6, No. 1, 75–97 (2003; Zbl 1033.03023)].Siberian Advances in Mathematics 01/2004; 14(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**Sufficient conditions are found for superintuitionistic logic to lack or possess the finite model property with respect to admissibility. For every superintuitionistic logic λ of width greater than 2 that possesses the co-cover property and the finite model property with respect to admissibility, a sequence R of admissible inference rules is constructed. This sequence has the following property: There is an r∈R admissible in λ but disprovable in some finite intuitionistic frame of width greater than 2.Reviewer: A. S. Morozov (Novosibirsk)Siberian Advances in Mathematics 01/2003; 13(2). -
##### Article: Morse functions on simple polyhedra and a related way of presenting special spines of manifolds

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**ABSTRACT:**The author introduces a notion of Morse type function on spines of three-dimensional manifolds. A criterion for a spine to be special is given in terms of the number of critical points of a Morse type function. A connection is revealed between the complexity of a manifold and the types of critical points of some fixed Morse function on its minimal spine. This is an English translation of the author’s article published in the book [Yu. G. Reshetnyak (ed.) et al., Proceedings of the conference ‘Geometry and applications’ dedicated to the 70th anniversary of Prof. Victor Toponogov. Novosibirsk: Izdatel’stvo Instituta Matematiki (2001; Zbl 1004.57017)].Reviewer: V. V. Vershinin (Novosibirsk)Siberian Advances in Mathematics 01/2003; 13(3).

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